1. Field of the Invention
The present invention relates in general to the field of information processing, and more specifically to a system and method for beamforming for non-collaborative, space division multiple access systems with transmitter and receiver antenna arrays.
2. Description of the Related Art
The demand for wireless communication systems continues to expand. Wireless communication systems transmit and receive signals within a designated electromagnetic frequency spectrum. The capacity of the electromagnetic frequency spectrum is limited. Thus, the usage expansion of wireless communication systems continually introduces challenges to improve spectrum usage efficiency. Space division multiple access (SDMA) represents one approach to improving spectrum usage efficiency. SDMA has recently emerged as a popular technique for the next generation communication systems. SDMA based methods have been adopted in several current emerging standards such as IEEE 802.16 and the 3rd Generation Partnership Project (3GPP).
FIG. 1 depicts a wireless communication system 100 that employs SDMA. The communication system 100 is a multiple-input multiple-output (MIMO) system. In MIMO systems, transmitters and receivers are both equipped with multiple antennas. The wireless communication system 100 includes multiple base stations (BS's) 102.1 through 102.p and multiple subscriber stations (SS's) 104.1-104.r, where “p” and “r” are integers representing the number of base stations and subscriber stations, respectively, in a given geographic area. Base stations and subscriber stations can be both transmitters and receivers when both base stations and subscriber stations are equipped with a receiver and a transmitter. Base stations generally communicate with multiple subscriber stations. Subscriber stations communicate directly with a base station and indirectly, via the base station, with other subscriber stations. The number of base stations depends in part on the geographic area to be served by the wireless communication system 100. Subscriber systems can be virtually any type of wireless one-way or two-way communication device such as a cellular telephones, wireless equipped computer systems, and wireless personal digital assistants. The signals communicated between base stations and subscriber stations can include voice, data, electronic mail, video, and other data, voice, and video signals.
In a MIMO system, each base station 102 and subscriber station 104 includes an array of antennas for transmitting and receiving signals. SDMA-MIMO wireless communication systems utilize a base station with an array of multiple antennas to transmit to and receive signals from subscriber stations. The antenna array forms a beam by applying a set of weights to signals applied to each antenna in the antenna array. A different set of beam forming weights is applied to communications between the base station and each subscriber station with a goal of minimizing interference between the radio communication devices signals. In some transmission schemes, such as time division duplex (TDD), beam forming between the base station and subscriber stations allows the allocation of the same frequency channel and different time channel to subscriber stations during downlink and uplink. In other transmission schemes, such as frequency division duplex (FDD), beam forming between the base station and subscriber stations allows the allocation of the same time channel and different frequency channel to subscriber stations during downlink and uplink. In SDMA, separation between different subscriber stations sharing the same time-frequency channel occurs in the spatial dimension.
FIG. 2 depicts base station 202 and subscriber stations 204.1 through 204.m in an SDMA, MIMO wireless communication system. Base station 202 represents each of base stations 102.1 through 102.p, and subscriber stations 204.1 through 204.m represent any group of m subscriber stations. MIMO systems use beamforming to transmit a single data stream through multiple antennas, and the receiver combines the received signal from the multiple receive antennas to reconstruct the transmitted data. In general, “beamforming” processes a signal using weight vector and an array of antennas to direct the signal using interference properties.
Base station 202 has an array of N antennas 206, where N is an integer greater than or equal to m. The base station prepares a transmission signal, represented by the vector xi, for each signal si, where iε{1, 2, . . . , m}. The transmission signal vector xi is determined in accordance with Equation [1]:xi=wi·si  [1]where wi, is the ith beamforming, N dimensional transmission weight vector (also referred to as a “transmit beamformer”), and each coefficient wj of weight vector wi represents a weight and phase shift on the jth antenna 206, where jε{1, 2, . . . , ki}, and ki represents the number of receiving antennas of the ith subscriber station 204.i. “si” is the data to be transmitted to the ith receiver. The coefficients of weight vector wi is often a complex weight. Unless otherwise indicated, transmission beamforming vectors are referred to as “weight vectors”, and reception vectors are referred to as “combining vectors”.
The transmission signal vector xi is transmitted via a channel represented by a channel matrix Hi. The channel matrix Hi represents a channel gain between the transmitter antenna array 206 and the ith subscriber station antenna array 208.i. Thus, the channel matrix Hi can be represented by a ki×N matrix of complex coefficients, where ki is the number of antennas in the ith subscriber station antenna array 208.i. The value of ki can be unique for each subscriber station. The coefficients of the channel matrix Hi depend, at least in part, on the transmission characteristics of the medium, such as air, through which a signal is transmitted. Several conventional methods exist to determine the channel matrix Hi coefficients. In at least one embodiment, a known pilot signal is transmitted to a receiver, and the receiver, knowing the pilot signal, estimates the coefficients of the channel matrix Hi using well-known pilot estimation techniques. In at least one embodiment, the actual channel matrix Hi is known to the receiver and may also be known to the transmitter.
Each subscriber station 204 receives signals on the antennas of each subscriber station. The received signals for the ith subscriber station 204.i are represented by a ki×1 received signal vector yi in accordance with Equation [2]:
                              y          i                =                                            s              i                        ⁢                          H              i              H                        ⁢                          w              i                                +                      (                                                            ∑                                      n                    =                    1                                    m                                ⁢                                                      s                    n                                    ⁢                                      H                    i                    H                                    ⁢                                      w                    n                                                              -                                                s                  i                                ⁢                                  H                  i                  H                                ⁢                                  w                  i                                                      )                                              [        2        ]            where “si” is the data to be transmitted to the ith subscriber station 204.i, “sn” is the data transmitted to the nth subscriber station 204.n, “HiH” represents the complex conjugate of the channel matrix correlating the subscriber station 204 and ith subscriber station 204.i, wi is the ith base station weight vector, and wn is the nth base station 202.n weight vector. The superscript “H” is used herein as a hermitian operator to represent a complex conjugate operator. The jth element of the received signal vector yi represents the signal received on the jth antenna of subscriber station 204.i, jε{1, 2, . . . , ki}. The first term on the right hand side of Equation [2] is the desired receive signal while the summation terms less the desired receive signal represent co-channel interference.
To obtain a data signal, zi, which is an estimate of the transmitted data si, the subscriber station 204.i combines the signals received on the k antennas using a combining vector vi in accordance with Equation [3]:zi=ŝi=viHyi  [3].
MIMO-SDMA communication methods can be classified into two major categories: (1) collaborative and (2) non-collaborative. Collaborative MIMO-SDMA methods entail all schemes where the weighting vectors wi and combining vectors vi of base station 202 and subscriber station 204.i are designed together in a collaborative fashion, i.e. the knowledge of MIMO channels to all the subscriber stations 204 are used centrally to jointly design the base station 202 weighting and combining vectors and each subscriber station 204. Non-collaborative methods on the other hand employ sequential design, i.e. either the base station 202 or the subscriber stations 204 design their weighting or combining vectors first and knowledge of the designed vectors are used to design the remaining set of vectors.
The signal throughput capacity of collaborative SDMA systems is conventionally greater than the capacity of non-collaborative systems since collaborative systems benefit from the joint knowledge of the channels Hi, iε{1, 2, . . . m}, to all the subscriber stations 204 while combining vectors for one subscriber station 204.i in the non-collaborative systems are determined independently of the other subscriber stations 204.
Collaborative systems exhibit downsides including:                Feed forward control information—SDMA systems involve feedback of some information from each subscriber station 204i to the base station 202 that allows a base station 202 to know or determine channel information. In collaborative systems, the base station 202 uses this channel information to design both the base station 202 and the subscriber station 204i beamforming weight vectors. The choice of the subscriber station 204.i weight vectors, however, needs to be conveyed to the subscriber station 204.i. Hence this weight vector information needs to be fed-forward to the individual subscriber station 204.i. Non-collaborative schemes, on the other hand, do not feed-forward information.        Feedback overhead—Both conventional collaborative and non-collaborative MIMO-SDMA systems require control channels to feedback MIMO channel information to the base station 202. While in the case of collaborative schemes the complete MIMO channel matrix needs to be fed back by each subscriber station 204.i, non-collaborative schemes which design the subscriber station 204.i beamforming combining vectors first need only feed back a vector corresponding to the projection of the subscriber station 204.i choice of a combining vector on to the MIMO channel matrix Hi. This considerably reduces the amount of feedback required with non-collaborative schemes.        
The downsides of collaborative systems can be non-trivial in terms of adversely affecting performance not only in terms of the volume of control information exchanged, but also, for example, in fast changing channel conditions where the cost of an extra bit of control information may cost more than just the size of a bit. Further, in wideband systems, such as orthogonal frequency division multiple access (OFDMA) systems, the feed forward has to be done, in the worst case, on a per subcarrier basis which can significantly increase the overheads of communication.
However, designing optimal beamforming weight vectors and combining vectors for non-collaborative systems has proven to be an obstacle for conventional systems. To improve signal-to-interference plus noise ratios (SINRs), communication systems attempt to design weight and combining vectors so that transmission signal xi does not interfere with any other transmission signal. In a non-collaborative system, if you design the combining vector vi first, the subscriber station 204.i transmits data to the base station so that the base station is aware of the combining vector vi. The base station 202 then designs the weight vector wi in light of the combining vector vi. However, the combining vector vi might not yield the optimal design for the weight vector wi. However, the combining vector vi cannot now change, because the weight vector wi would become incompatible. The weight vector wi can be designed first without knowing the combining vector vi; however, an acceptably high SINR is not guaranteed . Thus, a “catch-22” develops.